Hamiltonian formulation of Carrollian Maxwell theory in Deformed Light-cone Kaluza-Klein-like Null reduction

Abstract: We construct magnetic and electric Carrollian Maxwell theories by performing Kaluza-Klein-like null reduction of a complex Maxwell field in a Bargmann deformed light-cone background with manifest gauge symmetry. The procedure preserves a first-class U(1) Gauss constraint throughout the Carrollian limit. Gauge invariance is therefore maintained in our Hamiltonian formulation. By choosing different scalings, we obtain standard magnetic Carrollian theory and electric Carrollian theory. However, a scalar field could appear in the Carrollian theory in a coupled or decoupled way, which has not been found by previous methods. This result fully reveals the diversity of Carrollian theories accessible through the deformed light-cone Kaluza-Klein-like null reduction method. Furthermore, our work provides an explicit example of the correct application of this approach, thereby broadening the scope of its applicability to gauge theories.